Mathematical Research Letters

Volume 30 (2023)

Number 4

3-manifolds that bound no definite 4-manifolds

Pages: 1063 – 1080

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n4.a4

Authors

Marco Golla (Laboratoire de Mathématiques Jean Leray CNRS and Nantes Université, Nantes, France)

Kyle Larson (Department of Mathematics, University of Georgia, Athens, Ga., U.S.A.)

Abstract

We produce a rational homology 3‑sphere that does not smoothly bound either a positive or negative definite 4‑manifold. Such a 3‑manifold necessarily cannot be rational homology cobordant to a Seifert fibered space or any 3‑manifold obtained by Dehn surgery on a knot. The proof requires an analysis of short characteristic covectors in bimodular lattices.

Full Text (PDF format)

Received 7 January 2021

Received revised 23 June 2021

Accepted 28 July 2022

Published 3 April 2024